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Quantum Cryptography and Quantum Teleportation

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The Amazing World of Quantum Computing

Part of the book series: Undergraduate Lecture Notes in Physics ((ULNP))

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Abstract

This chapter is meant to be an appetizer and lightly relies on the reader’s intuition to understand the mathematical steps involved. The chapter directly introduces two quantum algorithms: (1) How to encrypt messages (cryptography), which if snooped upon during transmission to a recipient, will be detected; and (2) how to teleport the state of a quantum object. Along the way just enough intuitively understandable but weird and exclusive aspects of quantum mechanics as compared to classical mechanics are introduced.

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Notes

  1. 1.

    Feynman [15], Chap. 6.

  2. 2.

    Feynman [15].

  3. 3.

    Turing [31].

  4. 4.

    Wootters and Zurek [33].

  5. 5.

    As quoted in: Mermin [20]. “Einstein maintained that quantum metaphysics entails spooky actions at a distance; experiments have now shown that what bothered Einstein is not a debatable point but the observed behaviour of the real world.”

  6. 6.

    See the following three papers to develop a perspective on how physicists came to understand entanglement: Einstein et al. [14], Bell [6], and Aspect et al. [3].

  7. 7.

    All four postulates are formally described in Chap. 2, Sect. 2.7.

  8. 8.

    Schumacher [26].

  9. 9.

    See Barenco et al. [4]. See also Chap. 7 of this book.

  10. 10.

    Developed by Gilbert S. Vernam of AT&T. This is the only known totally secure cypher. Vernam was granted a patent protecting the cypher: Secret Signaling System. US Patent No. 1,310, 719, patented July 22, 1919.

  11. 11.

    Shannon [27]. See also: Goldreich [18]; Black et al. [9], pp. 189–244, Sect. 5.

  12. 12.

    Rivest et al. [25]. See also: Allenby and Redfern [2]. Rivest, Shamir, and Adleman received the Turing award for 2002 for their contributions to public key cryptography . http://www.acm.org/announcements/turing_2002.html.

  13. 13.

    Bennett and Brassard [7]. The first quantum cryptography ideas were proposed by Stephen Wiesner in the late 1960s, but unfortunately were not accepted for publication at the time! It was eventually published in 1983, Wiesner [32]. Bennett and Brassard built upon Wiesner’s work. A simple proof of the security of the BB84 protocol was provided by Shor and Preskill [28]. See also: Brassard and Crépeau [11] and Brassard [10].

  14. 14.

    Qiu [23]. See also: Muralidharan [21].

  15. 15.

    Giles [17].

  16. 16.

    Bennett et al. [8].

  17. 17.

    Riebe et al. [24] and Barrett et al. [5].

  18. 18.

    Polzik et al. [22].

  19. 19.

    Bussieres et al. [12].

  20. 20.

    Tsurumoto et al. [30].

  21. 21.

    See, e.g., Alba [1] and Gibney [16].

  22. 22.

    Castelvecchi [13].

  23. 23.

    For an easy to understand reference for eigenvalues and eigenvectors, see Chap. 6, http://math.mit.edu/~gs/linearalgebra/ila0601.pdf in Strang [29].

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    Rajendra K. Bera

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Bera, R.K. (2020). Quantum Cryptography and Quantum Teleportation. In: The Amazing World of Quantum Computing. Undergraduate Lecture Notes in Physics. Springer, Singapore. https://doi.org/10.1007/978-981-15-2471-4_1

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